Since angles ACB and BCD are supplementary, their measures add up to 180 degrees.
Given:
- m∠ACB = (x + 28)°
- m∠BCD = (x + 48)°
We can set up the equation:
\[ m∠ACB + m∠BCD = 180° \]
Substituting in the expressions for the angles:
\[ (x + 28) + (x + 48) = 180 \]
Combining like terms:
\[ 2x + 76 = 180 \]
Now, subtract 76 from both sides:
\[ 2x = 104 \]
Dividing both sides by 2 gives:
\[ x = 52 \]
Now, substituting \(x\) back into the expression for m∠BCD:
\[ m∠BCD = x + 48 = 52 + 48 = 100° \]
Therefore, the correct answer is:
100°.